The US has raised repeated concerns about security at the London Olympics and is preparing to send up to 1,000 of its agents, including 500 from the FBI, to provide protection for America's contestants and diplomats, the Guardian has learned.

American officials have expressed deep unease that the UK has had to restrict the scope of anti-terrorism "stop and search" powers, and have sought a breakdown of the number of British police and other security personnel that will be available next summer.

The prime minister and other senior members of the cabinet, including home secretary Theresa May and culture and sport secretary Jeremy Hunt, are taking turns to chair security meetings about the Olympics, which are often dominated by the latest questions from the US, sources said. But Washington's need for reassurance is exasperating British officials and anti-terrorism officials, who have privately raised concerns about the meddling, as well as the size of the US "footprint" in the UK during the games next year.

"We are not equal partners in this," said one security official. "They are being very demanding."

The friction is adding to the pressures on the London Organising Committee of the Olympic and Paralympic Games (Locog), which is responsible for preparing and staging the event. The Guardian has learned the committee is attempting to resolve a potential crisis over venue security, after conceding it had underestimated the number of security guards needed at the 32 sites across the country. Originally it had thought 10,000 guards would be enough, but after a review over the summer it now believes it will need up to 21,000.

Venue safety is not the responsibility of the police, so the firm G4S was awarded the contract to find and train the initial group. The company will this week begin an advertising campaign to meet that target. But the organising committee does not have the money to pay G4S to make up the shortfall, and does not believe the firm has enough time to do so, forcing ministers to turn to the Ministry of Defence for help.

The MoD has offered 3,000 soldiers, and another 2,000 in reserve – half the total required. The ministry is working within its own tight budget, and the late request for help has irritated some officials.

"What have they been doing for the last five years?" asked one. "There is less than a year to go and they've only just realised they need twice the number of security guards they first thought. Where is the money to pay for this coming from? It is an extra burden on the defence budget that we could well do without."

Another source said: "Everyone has now realised 10,000 was an underestimate. This is one of the biggest problems facing the Olympic authorities because there is an absolute dearth of vetted and qualified private security guards. Senior police had advised ministers and the committee that 10,000 was too few, but nobody wanted to listen because of the cost involved.

"The military will have to stand up some people. Otherwise G4S have got the Olympic committee over a barrel."

The problem will do little to reassure Washington, which will be supplementing its FBI personnel with an equal number of diplomatic security officials, some of whom will be armed. Though the UK's Joint Terrorism Analysis Centre has lowered the threat of attack to "substantial" – the third level on the scale – western intelligence agencies remain wary.

They know it is possible that al-Qaida, or one of its affiliates, may attempt to disrupt the Olympics, with members of the US team being obvious targets.

The Home Office and Scotland Yard believe the UK has a robust security strategy, but this has not stopped American officials voicing their concerns.

The police response to the London riots, the arrest of a security guard at the London Olympics site earlier this year, and the arrests made shortly before the visit of the Pope last year have provoked anxiety among US officials. The repeal of section 44 of the Terrorism Act, which allowed police to stop and search suspects with near impunity, also raised alarm. One well-placed Whitehall source said the entire Olympic security operation was being prepared "with the US in mind", adding: "The US will have no qualms in saying it is unsafe. If something happens and we say we did not have enough people, we are finished."

Another official said: "The Americans are risk-averse, with a capital A and underlined. They want to see everything. We are not equal partners in this. They want to be on top of everything – building protection, counter-terrorism strategy and VIP security – everything." Asked about the size of the US contingent heading to London next year, the official said: "They don't do things by halves."

In addition to the official American security entourage, the sponsors of the Games, including Coca-Cola, will have their own private security details, adding to the complexity of the policing operation.

The Ministry of Defence and the Home Office said no final decisions had been taken on the number of soldiers that might be needed to beef up security at some of the Olympic sites.An official said the need for an increase at the venues had become apparent when the Olympic committee began to role-play scenarios at some of the completed sites over the summer.

"The focus of the government and everyone involved is to deliver a safe and secure Olympic and Paralympic Games that London, the UK and the world can enjoy," a government spokesman said.

"Ministers and officials from across government are working closely with the police and Locog to ensure we have a robust safety and security strategy."

Officials said ministers, the Olympic committee and G4S were working together "to finalise the requirements for Olympic venue security". "As with all significant national events, we will make the best and most appropriate use of available resources," a statement said. "The Ministry of Defence have been fully involved in supporting Olympic security planning work."

G4S said it was confident of recruiting 10,000 security guards, and could recruit more, as long as the Olympic authorities gave the company enough time. "We need to know as soon as possible," said a spokesman.

The US state department declined to comment.

Locog said detailed security plans were being drawn up in collaboration with the government and security agencies.